If they are going to be private and not view-able by the majority of players, plus you can hide them from any possible readers, then why post them at all? Why not just use it to check their perception and delete the rolls and narrate what they do or don't see as a result.

You can also roll physical dice on your table, then.
Using private tags for hidden roll allows to remove those tags in case players ask for it - but that's personal preference, in the end.
There might be a situation where I as player ask the the GM to show the dice he rolled. If the GM then says he used the preview function to roll, it would leave a bad taste for me.

Also, there is no way to hide anything in a a game forum from a

meaning, a user accepted as 'reader' of a game, not someone just reading the forum

if you just use the preview and delete it, there is no actual record of the roll... meaning you are actually dictating as far as a reader is concerned, which of course, is fine, provided that is your style, but to be at all fair in your dealings with players and readers one must actually log the dice into the post. As dalar said, there are ways of cheating the players, but it's just not worth it and readers will see that anyway.

The only way to have logged dice on record without cheat tags is to actually roll them in the post.

Personally, I advise against even rolling on the table top. It looks way more pro to the players to roll everything they can see and for the readers to see that you roll other things as well. It also shows as a GM that you're far more concerned with running an interesting game than protecting your own plot, and even if the players don't see the rolls, it will come across in your GMing and they will get more of a feel that what they actually do as players will matter.

Of course transparency doesn't fix anything, but it lets everyone know they can keep you honest if a question should ever arise, and again, that's a psychological advantage for the game, not a mechanical one. Without transparency, the potential for such questions to arise becomes exponentially greater.

Personally I am a fan of the idea that an ounce of prevention is worth a pound of cure. Best not to let things have the potential to devolve if you can reasonably help it.

Again though, we're branching into the philosophy of rolling dice rather than the pure mechanics the thread was intended to discuss, and worse, the philosophy doesn't allow for one "right" answer, just a bunch of different schools of thought.

Over all I think the public rolling system is the best balance, but ymmv.